The shock peakon wave solutions of the general Degasperis–Procesi equation

This research paper applies the modified Khater method and the generalized Kudryashov method to the general Degasperis–Procesi (DP) equation, which is used to describe the dynamical behavior of the...

[1]  Hadi Rezazadeh,et al.  New solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity , 2018, Optik.

[2]  M. Eslami,et al.  A sub-equation method for solving the cubic–quartic NLSE with the Kerr law nonlinearity , 2019, Modern Physics Letters B.

[3]  B. R. Wong,et al.  Mitigating Internet bottleneck with fractional temporal evolution of optical solitons having quadratic–cubic nonlinearity , 2018, Optik.

[4]  Xiangyu Wang,et al.  Hamiltonian analysis of a hydro-energy generation system in the transient of sudden load increasing , 2017 .

[5]  M. Kaplan,et al.  A generalized Kudryashov method to some nonlinear evolution equations in mathematical physics , 2016 .

[6]  A. Constantin,et al.  The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations , 2007, 0709.0905.

[7]  Fairouz Tchier,et al.  Soliton solutions and conservation laws for lossy nonlinear transmission line equation , 2017 .

[8]  Mostafa Eslami,et al.  Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations , 2016, Appl. Math. Comput..

[9]  Abdul-Majid Wazwaz,et al.  An efficient algorithm to construct multi-soliton rational solutions of the (2+ 1)-dimensional KdV equation with variable coefficients , 2018, Appl. Math. Comput..

[10]  Mostafa M. A. Khater,et al.  Bifurcations of traveling wave solutions for Dodd–Bullough–Mikhailov equation and coupled Higgs equation and their applications , 2017 .

[11]  Jin Li,et al.  Rogue waves, bright-dark solitons and traveling wave solutions of the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation , 2018, Comput. Math. Appl..

[12]  Peter J. Olver,et al.  Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system , 1996 .

[13]  Darryl D. Holm,et al.  A New Integrable Equation with Peakon Solutions , 2002, nlin/0205023.

[14]  Rostam K. Saeed,et al.  Oblique optical solutions of mitigating internet bottleneck with quadratic-cubic nonlinearity , 2019, International Journal of Modern Physics B.

[15]  A. Wazwaz.  Solitary wave solutions for modified forms of Degasperis Procesi and Camassa Holm equations , 2006 .

[16]  R. Ansari,et al.  New exact solutions of nonlinear conformable time-fractional Boussinesq equations using the modified Kudryashov method , 2017 .

[17]  G. Perla Menzala,et al.  Existence and Uniqueness for Periodic Solutions of the Benjamin–Bona–Mahony Equation , 1977 .

[18]  Jian‐Guo Liu,et al.  Rational solutions and lump solutions to a non-isospectral and generalized variable-coefficient Kadomtsev–Petviashvili equation , 2018, Nonlinear Dynamics.

[19]  Vladimir S. Novikov,et al.  Perturbative symmetry approach , 2002, nlin/0203055.

[20]  Jing Ping Wang,et al.  Prolongation algebras and Hamiltonian operators for peakon equations , 2003 .

[21]  Rossen I. Ivanov,et al.  On the Integrability of a Class of Nonlinear Dispersive Wave Equations , 2005, nlin/0606046.

[22]  Dumitru Baleanu,et al.  On exact traveling-wave solutions for local fractional Korteweg-de Vries equation. , 2016, Chaos.

[23]  D. Baleanu,et al.  Time-fractional Cahn–Allen and time-fractional Klein–Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis , 2018 .

[24]  Ahmet Bekir,et al.  Bright and dark soliton solutions for some nonlinear fractional differential equations , 2016 .

[25]  M. Eslami,et al.  The propagation of waves in thin-film ferroelectric materials , 2019, Pramana.

[26]  Ahmet Bekir,et al.  On traveling wave solutions to combined KdV–mKdV equation and modified Burgers–KdV equation , 2009 .

[27]  Reza Ansari,et al.  New exact solutions of the conformable time-fractional Cahn–Allen and Cahn–Hilliard equations using the modified Kudryashov method , 2017 .

[28]  R. Ivanov,et al.  Water waves and integrability , 2007, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[29]  Mostafa M. A. Khater,et al.  Explicit Lump Solitary Wave of Certain Interesting (3+1)-Dimensional Waves in Physics via Some Recent Traveling Wave Methods , 2019, Entropy.

[30]  M. Eslami,et al.  The extended modified method applied to optical solitons solutions in birefringent fibers with weak nonlocal nonlinearity and four wave mixing , 2019, Chinese Journal of Physics.

[31]  E. Y. Bejarbaneh,et al.  New Exact Traveling Wave Solutions of the Unstable Nonlinear Schrödinger Equations , 2017 .

[32]  Yoshimasa Matsuno,et al.  The N-soliton solution of the Degasperis–Procesi equation , 2005, nlin/0511029.

[33]  D. Baleanu,et al.  Traveling wave solutions and conservation laws for nonlinear evolution equation , 2018 .

[34]  Z. Zong,et al.  Solving shock wave with discontinuity by enhanced differential transform method (EDTM) , 2012 .

[35]  Ahmet Bekir,et al.  Application of the Exp-function method for nonlinear differential-difference equations , 2010, Appl. Math. Comput..

[36]  A. Yusuf,et al.  Dark optical, singular solitons and conservation laws to the nonlinear Schrödinger’s equation with spatio-temporal dispersion , 2017 .

[37]  Saeid Abbasbandy,et al.  The first integral method for modified Benjamin–Bona–Mahony equation , 2010 .

[38]  H. Rezazadeh,et al.  Analytical study of resonant optical solitons with variable coefficients in Kerr and non-Kerr law media , 2019, Optical and Quantum Electronics.

[39]  Hans Lundmark,et al.  Formation and Dynamics of Shock Waves in the Degasperis-Procesi Equation , 2007, J. Nonlinear Sci..

[40]  Ahmet Bekir,et al.  Analytic solutions of the (2 + 1)-dimensional nonlinear evolution equations using the sine-cosine method , 2009, Appl. Math. Comput..

[41]  A. Bressan,et al.  Global Conservative Solutions of the Camassa–Holm Equation , 2007 .

[42]  Lixin Tian,et al.  Shock-peakon and shock-compacton solutions for K(p,q) equation by variational iteration method , 2007 .

[43]  M. Eslami,et al.  A large family of optical solutions to Kundu–Eckhaus model by a new auxiliary equation method , 2019, Optical and Quantum Electronics.

[44]  H. Rezazadeh,et al.  Optical solitons in nematic liquid crystals with Kerr and parabolic law nonlinearities , 2019, Optical and Quantum Electronics.

[45]  R. Johnson,et al.  The Classical Problem of Water Waves: a Reservoir of Integrable and Nearly-Integrable Equations , 2003 .

[46]  Mostafa M. A. Khater,et al.  Lump soliton wave solutions for the (2+1)-dimensional Konopelchenko–Dubrovsky equation and KdV equation , 2019, Modern Physics Letters B.

[47]  M. S. Osman,et al.  On complex wave solutions governed by the 2D Ginzburg–Landau equation with variable coefficients , 2018 .

[48]  M. Kaplan,et al.  New exact traveling wave solutions of the Tzitzéica-type evolution equations arising in non-linear optics , 2017 .

[49]  G. Swaters,et al.  Introduction to Hamiltonian Fluid Dynamics and Stability Theory , 1999 .

[50]  General Degasperis-Procesi equation and its solitary wave solutions , 2019, Chaos, Solitons & Fractals.

[51]  Mostafa M. A. Khater,et al.  Modified Auxiliary Equation Method versus Three Nonlinear Fractional Biological Models in Present Explicit Wave Solutions , 2018, Mathematical and Computational Applications.